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<p>In this study, we present an implicit incompressible smoothed particle hydrodynamics method designed for simulating fluid dynamics problems where rotational behavior is a key feature of the flow. Crucial to this task is the calculation of the viscous term of the Navier–Stoker equation, because most SPH operators for the Laplacian of velocity are either highly inaccurate or produce spurious resistance to rotation. Here, we introduce a novel equation for calculating the Laplacian of velocity, designed as a compromise between mathematical accuracy and the local conservation of angular momentum. The proposed method is validated through a series of simulations of the coiling behavior of highly viscous fluids, demonstrating its ability to naturally generate this phenomenon and accurately predict the cessation of coiling at appropriate heights. In addition, we validate the proposed method in terms of quantitatively reproduce the angular frequency of the coiling for different values of height with satisfactory results.</p>

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Implicit incompressible SPH(2) with novel Laplacian of velocity operator for highly viscous rotational problems

  • 期刊论文

  • 发表日期：

    2025年12月20日

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  • Daniel S. Morikawa,
  • Mitsuteru Asai

摘要

In this study, we present an implicit incompressible smoothed particle hydrodynamics method designed for simulating fluid dynamics problems where rotational behavior is a key feature of the flow. Crucial to this task is the calculation of the viscous term of the Navier–Stoker equation, because most SPH operators for the Laplacian of velocity are either highly inaccurate or produce spurious resistance to rotation. Here, we introduce a novel equation for calculating the Laplacian of velocity, designed as a compromise between mathematical accuracy and the local conservation of angular momentum. The proposed method is validated through a series of simulations of the coiling behavior of highly viscous fluids, demonstrating its ability to naturally generate this phenomenon and accurately predict the cessation of coiling at appropriate heights. In addition, we validate the proposed method in terms of quantitatively reproduce the angular frequency of the coiling for different values of height with satisfactory results.